In his first-ever interview, the sole Australian survivor of the Waco siege has revealed to 60 Minutes what really took place during the 51-day stand-off, and why he believes crazed cult leader David Koresh will one day return to Earth as the son of God.

"Found out thru (sic) Snapchat my friend Amanda Alvear was there at Pulse last night," he wrote alongside the video.

"Tried calling and texting and still haven't gotten a reply."

Ms Alvear was among the first group of victims named after the tragedy.

Before Ms Alvear's death was confirmed, her brother, Brian Alvear, said the last he heard was that she was hiding in a bathroom as the gunman shot at patrons indiscriminately.

Family and friends of victims trapped in the nightclub have waited anxiously to find out whether their loved ones are among the 50 people killed and 53 wounded.

Overnight, the FBI and other law enforcement authorities were poring over evidence that could explain the motives for the rampage, a massacre that President Barack Obama denounced as an act of terror and hate.

Mateen, 29, a New York-born Florida resident and US citizen who was the son of Afghan immigrants, was shot and killed by police who stormed the club with armoured cars after a three-hour siege.

Mateen had called emergency services during the shooting and pledged allegiance to the leader of the militant Islamic State group, officials said.

His father said on Sunday his son was not radicalised, but indicated Mateen had strong anti-gay feelings. His ex-wife described him as mentally unstable and violent toward her.

Islamic State reiterated overnight a claim of responsibility for the attack.

"One of the Caliphate's soldiers in America carried out a security invasion where he was able to enter a crusader gathering at a nightclub for homosexuals in Orlando, Florida ... where he killed and injured more than a hundred of them before he was killed," the group said in a broadcast on its Albayan Radio.

Although the group claimed responsibility, this did not necessarily mean it directed the attack: there was nothing in the claim indicating coordination between the gunman and Islamic State before the rampage.

The attack reignited the debate over how best to confront violent Islamist militancy, a top issue in the November 8 presidential election campaign.

Democratic candidate Hillary Clinton and her Republican rival Donald Trump were both expected to address the issue on Monday.

'This guy was pretty screwed up

The shooting began just after 2am on Sunday at the crowded Pulse nightclub in the heart of Orlando, about 25km northeast of the Walt Disney World Resort.

Some 350 patrons were attending a Latin music event at the club, a well-known gay nightspot in the city, and survivors described scenes of carnage and pandemonium as the shooter took hostages inside a bathroom.

Nearly 24 hours after the rampage ended, authorities had publicly named only 21 of the victims, half of whom were in their 20s.

Family and friends waited for news outside a centre in Orlando where authorities were gathering details about people still missing.

Despite Mateen's 911 call expressing support for Islamic State, US officials said on Sunday they had no conclusive evidence of any direct connection with foreign extremists.

"So far as we know at this time, his first direct contact was a pledge of bayat (loyalty) he made during the massacre," said a US counterterrorism official.

"This guy appears to have been pretty screwed up without any help from anybody."

Authorities said Mateen had been twice questioned by FBI agents in 2013 and 2014 after making comments to co-workers about supporting militant groups, but neither interview led to evidence of criminal activity.

Ronald Hopper, the FBI's assistant special agent in charge on the case, said Mateen was questioned in 2014 about his contacts with Moner Mohammad Abu-Salha, a US citizen who also had lived in Florida and became a suicide bomber in Syria that year.

Mateen's former wife, Sitora Yusufiy, said he was emotionally and mentally disturbed, yet aspired to be a police officer.

Yusufiy told reporters near Boulder, Colorado, that she had been beaten by Mateen during outbursts of temper in which he would "express hatred towards everything".

But his father Mir Siddique, who saw Mateen on Saturday afternoon, said he saw nothing out of the ordinary.

"Everything was normal," Siddique told ABC News, saying his son was not radicalised.

"He was just a regular person who went to work, coming back and take care of his wife and his kids," he said. "If he was alive, I would ask him one question: why?"

In an interview with NBC news, the father described an incident in downtown Miami in which his son saw two men kissing in front of his wife and child and became very angry.

Mateen and his family regularly attended a Florida mosque.

On Sunday night, federal agents combed through Mateen's apartment in the Atlantic coast town of Fort Pierce, about 190km southeast of Orlando, as numerous evidence vans sat parked outside.